Uniqueness of Instantaneously Complete Ricci flows

TL;DR

This paper proves the uniqueness of instantaneously complete Ricci flows on surfaces without requiring bounds on curvature or growth, completing the well-posedness theory for such flows.

Contribution

It establishes the uniqueness of instantaneously complete Ricci flows on surfaces under minimal assumptions, advancing the mathematical understanding of Ricci flow behavior.

Findings

Proves uniqueness without curvature bounds

Completes the well-posedness theory for these flows

Builds on previous foundational work

Abstract

We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, particularly [23, 11], this completes the well-posedness theory for instantaneously complete Ricci flows on surfaces.